Trying to estimate the spectral density \(f\)  from a single path of a SRH \(S\alpha S\)  process, determining the non-ergodic almost sure limit of empirical functions is essential.
We make use of the following LePage type series representation of \(X\)  which stems from the series representation of complex \(S\alpha S\)  random measures [1]}.
As a consequence, SRH \(S\alpha S\)  processes are in fact conditionally Gaussian which allows us to use their underlying Gaussian structure for further analysis.
